Abstract

Capturing key electronic properties such as charge excitation gaps within models at or above the atomic scale presents an ongoing challenge to understanding molecular, nanoscale, and condensed phase systems. One strategy is to describe the system in terms of properties of interacting material fragments, but it is unclear how to accomplish this for charge-excitation and charge-transfer phenomena. Hamiltonian models such as the Hubbard model provide formal frameworks for analyzing gap properties but are couched purely in terms of states of electrons, rather than the states of the fragments at the scale of interest. The recently introduced Fragment Hamiltonian (FH) model uses fragments in different charge states as its building blocks, enabling a uniform, quantum-mechanical treatment that captures the charge-excitation gap. These gaps are preserved in terms of inter-fragment charge-transferhopping integrals T and on-fragment parameters U(FH). The FH model generalizes the standard Hubbard model (a single intra-band hopping integral t and on-site repulsion U) from quantum states for electrons to quantum states for fragments. We demonstrate that even for simple two-fragment and multi-fragment systems, gap closure is enabled once T exceeds the threshold set by U(FH), thus providing new insight into the nature of metal-insulator transitions. This result is in contrast to the standard Hubbard model for 1d rings, for which Lieb and Wu proved that gap closure was impossible, regardless of the choices for t and U.

Work performed at Los Alamos National Laboratory was under the auspices of the U.S. Department of Energy, under Contract No. DE-AC52-06NA25396. Partial funding was provided by the Center for Materials at Irradiation and Mechanical Extremes, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. 2008LANL1026. Partial funding was also provided by Laboratory Directed Research and Development Program. Work performed at the University of New Mexico was under the auspices of the Center for Materials at Irradiation and Mechanical Extremes and the DoD/DTRA CB Basic Research Program under Grant No. HDTRA1-09-1-008. Thanks are extended to Anders Niklasson, Richard L. Martin, Ramamurthy Ramprasad, and Jian-Xin Zhu for commenting on the manuscript.

Abstract

Capturing key electronic properties such as charge excitation gaps within models at or above the atomic scale presents an ongoing challenge to understanding molecular, nanoscale, and condensed phase systems. One strategy is to describe the system in terms of properties of interacting material fragments, but it is unclear how to accomplish this for charge-excitation and charge-transfer phenomena. Hamiltonian models such as the Hubbard model provide formal frameworks for analyzing gap properties but are couched purely in terms of states of electrons, rather than the states of the fragments at the scale of interest. The recently introduced Fragment Hamiltonian (FH) model uses fragments in different charge states as its building blocks, enabling a uniform, quantum-mechanical treatment that captures the charge-excitation gap. These gaps are preserved in terms of inter-fragment charge-transferhopping integrals T and on-fragment parameters U(FH). The FH model generalizes the standard Hubbard model (a single intra-band hopping integral t and on-site repulsion U) from quantum states for electrons to quantum states for fragments. We demonstrate that even for simple two-fragment and multi-fragment systems, gap closure is enabled once T exceeds the threshold set by U(FH), thus providing new insight into the nature of metal-insulator transitions. This result is in contrast to the standard Hubbard model for 1d rings, for which Lieb and Wu proved that gap closure was impossible, regardless of the choices for t and U.